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A used-book seller purchased 50 copies of a book for a total of

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A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 07:41
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A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 07:46
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATinsight, GMATGuruNY,
Could you help me to cross out wrong choices with logically other than algebraic method?

Thanks__
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 08:02
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

Let m = 100

So, CP of each book is 2

SP of each book is 125% of 2 => 2.50

Now, check the options Answer must be (C) m/40
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 10:07
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A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

Could you help me to cross out wrong choices with logically other than algebraic method?

You shouldn't be trying to do most math problems by "process of elimination"; that's often impossible, and when it's not, it's often much more time-consuming than just solving the problem. Here, each book costs the seller m/50 euros. Then each book is sold for 25% more than that, so for 1.25m/50 euros. You can now simplify, or glance at the answers and see that only m/40 could possibly equal 1.25m/50.

If you instead wanted to use "process of elimination", you could notice the larger m is, the more the books cost the seller, so the more each book will sell for. From there it must be true that m is in the numerator of the right answer, and not in the denominator. That eliminates answer E. But in the time it took to eliminate just one answer choice, we could have solved the problem completely. Any other logical technique you care to use to eliminate other wrong answers requires you to notice that you'll divide (and not multiply) m by the '50', and if you're doing that, you're essentially solving the problem anyway.
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A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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Updated on: 13 May 2020, 19:33
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

The cost of 50 books is m Euros.
The selling price of all 50 books is going to be 25% more than m or 1.25m or $$\frac{5m}{4}$$.
The, cost of 1 book will be,
$$\frac{5m}{4*50}$$
= $$\frac{m}{40}$$
Therefore, C) $$\frac{m}{40}$$

Thanks to GMATinsight for pointing out the error earlier.

Originally posted by CoachNikhilesh on 13 May 2020, 18:31.
Last edited by CoachNikhilesh on 13 May 2020, 19:33, edited 1 time in total.
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 18:51
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A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

50 copies for a total of m euros
i.e. cost per copy = m/50

Now, she sold each copy for a price which is 25% more than purchase price

i.e. Selling price = 125% of cost = (125/100)*cost = (5/4)*(m/50) = m/40 euros

Asad This is a simple problem in which it is suggested that "we follow the same calclation which the question clearly asks" If question expects you to calculate price per copy then don't deviate for any short answer, just take it that way algebraically

The method using the values has been well explained by Abhishek009 so I would recommend taking m = 100 and solving the question just because 100 is divisible by 50
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 18:52
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CoachNikhilesh wrote:
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

It doesn't matter how many book are there.
The cost of one book is m Euros.
The selling price of one book is going to be 25% more than m or 1.25m
1.25m = $$\frac{5m}{4}$$
Therefore, B

CoachNikhilesh

Please check the two highlighted parts. I guess quick reading has resulted in misinterpretation of information.
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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13 May 2020, 20:49
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

purchase price per book = m/50

selling price per copy = 1.25(m/50) = m/40

IMO C
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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14 May 2020, 02:56
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATinsight, GMATGuruNY,
Could you help me to cross out wrong choices with logically other than algebraic method?

Thanks__

Depending on one strategy to solve a question is akin to depending on a revolver to win you a gun fight. It may win you some battles but not all. Learn to apply a combination of strategies in a question rather than stereotyping them into silos.

Also, remember that there is no magic sauce to decide which strategy to apply in which question. This has to happen based on your practice and on your sense of judgement.

Since the total money spent was m, m has to come in the numerator. Therefore, options having m in the denominator are wrong. Option E can be eliminated.
Since each book is being sold for 25% more, the cost of each book has to be multiplied with 1.25. Therefore, option D doesn’t make any sense in the scheme of things and can be eliminated.

Beyond this stage, it’s pointless to invest time on finding out a logic based on which you want to eliminate options. You’re better off investing time in solving the question using Algebra. Plugging in for m may be another strategy that you wan’t to employ at this stage.

If m = 500, each book costed 10 euros. Adding a profit of 25%, each book was sold for 12.5 euros. Plug in 500 in each of the remaining options and see which one gives you 12.5.

Answer option A is $$m/4$$ which is 125. Eliminate.

Answer option B is $$\frac{5m}{4}$$ which is 625. Eliminate.

Answer option C is $$\frac{m}{40}$$ which is 12.5. This is the correct answer.

Hope that helps!
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Re: A used-book seller purchased 50 copies of a book for a total of  [#permalink]

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16 May 2020, 08:06
A used-book seller purchased 50 copies of a book for a total of $$m$$ euros. She then sold each book for 25 percent more than her original per-book purchase price. In terms of $$m$$, for how many euros did sell each book?
A) $$\frac{m}{4}$$
B) $$\frac{5m}{4}$$
C) $$\frac{m}{40}$$
D) $$125m$$
E) $$\frac{125}{2m}$$

The cost per book was m/50, so each book was sold for m/50 * 5/4 = 5m/200 = m/40.

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Re: A used-book seller purchased 50 copies of a book for a total of   [#permalink] 16 May 2020, 08:06